$10\mathrm{.}6$ For the beam section shown, the yield stress is $350$MPa and the modulus of elasticity is $200$GPa. $($a$)$ Calculate the elastic moment capacity and the radius of curvature at that moment. $($b$)$ Calculate the plastic moment and shape factor. $($c$)$ Calculate the moment and the radius of curvature when the $6030mm$ elements are fully yielded and the $120120mm$ element remains elastic. $($d$)$ Calculate the residual stresses when the moment in part $($c$)$ is removed. $[($a$)147$ kN$.$m$,51\mathrm{.}4$ m; $($b$)246$ kN$.$m$,1\mathrm{.}67$; $($c$)195$ kN$.$m$,34\mathrm{.}3$ m;

$($d$)$ at $y=60mm$:$-40$MPa, at $y=90mm$:$115$MPa$]$